Question

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm. What is the approximate difference between m∠C and m∠A? 34.8° 44.8° 46.3° 47.9°

Answer 1

44.8 is the answer

Step-by-step explanation:

Answer 2

Answer:
`44.8\°`

Step-by-step explanation:

We have a right triangle with sides AB, BC=5cm and AC=13cm (the hypotenuse). Let's apply the Pithagorean Theorem to find AB:

`AC^(2)=AB^(2) + BC^(2)` (1)

`AB^(2)=AC^(2) - BC^(2)` (2)

`AB^(2)=(13cm)^(2) - (5cm)^(2)` (3)

`AB=12cm` (4)

Now that we know the value of each side of the triangle, we will use the trigonometric function sine to find the angles C and A (angle B is
`90\°` remembering we are talking about a right triangle):

For angle C:

`sinC=(Oppositeside)/(Hypotenuse)`

`sinC=(12)/(13)` (5)

`C=sin^(-1)((12)/(13))` (6)

`C=67.38\°` (7)

For angle A:

`sinA=(5)/(13)` (8)

`A=sin^(-1)((5)/(13))` (9)

`A=22.62\°` (10)

Calculating the difference between both angles:

`C-A=67.38\°- 22.62\°`

`C-A=44.76\° \approx 44.8\°`